Liquid container



July 12, 1966 J. ca. sues 3,260,399

LIQUID CONTAINER Filed April 25, 1963 fiE- INVENTOR. (/ACK 6n 5/5-5 to be positioned above a supporting surface.

United States Patent 3,260,399 LIQUID CONTAINER Jack G. Sieg, 4602 E. 51st St., Tulsa 35, ()kla. Filed Apr. 25, 1963, Ser. No. 275,723 2 Claims. (Cl. 22018) This invention relates generally to improvements in liquid containers, and more particularly, but not by way of limitation, to structures particularly adapted to contain a liquid above a supporting surface.

In the past it has been known to provide liquid containers, such as wading or play pools, which were adapted A typical wading tank or play pool included a large, shallow, flexible container having a bottom and side walls and being composed of a waterproof material, such as plastic or the like. A suitable framework for supporting such a flexible container was provided bya plurality of elongated tubular sections which were connected together by suitable coupling members so that an upwardly extending tubular frame was constructed. The flexible container was connected to the tubular framework at a plurality of points. Although the flexible container was connected to the framework along its upper edge, lateral support for the liquid held by the container was provided by a plurality of upright tubular members of the framework which braced the flexible container. It is apparent that a liquid container having such a construction required a framework that was constructed sufficiently rugged to withstand the lateral pressure of the contained liquid.

If the depth of the liquid held in an above-the-ground container was greater than that of a relatively shallow play pool, or the like, it was necessary to provide bracing members extending outwardly from the framework for engagement with the ground or other supporting surface in use, and cooperating with sloping brace members which assisted in supporting the upright members of the framework against the lateral pressure of the contained liquid. For an above-the-ground liquid container as large as a swimming pool, it was necessary to construct the liquid container from a heavy gauge rigid material, such as sheet steel or the like, which was able to Withstand the lateral pressure of the contained liquid in the areas between the upright members. Furthermore, it was necessary to provide complicated side braces which cooperated with members, such as stakes, driven into the supporting surface for additional lateral support. It will also be evident that the complicated bracing required for a relatively large abovethe-ground liquid container greatly increased the cost of installation of such a container, both in the cost of the materials involved, and in the cost of the labor required to install the necessary framework and braces. It is also apparent that if the liquid container itself was constructed of a heavy gauge, rigid material, that such a construction presented a problem in the storage of the container when use thereof Was not desired.

It has also been known, heretofore, to provide structures for containing large volumes of liquid, such as drilling mud or the like, above a supporting surface. Such a tank comprised a flexible inner container which was supported by a suitable outer framework. In some instances, an upwardly extending pole was secured to the floor inside the flexible container so that a plurality of circumferentially spaced, supporting tension members could be secured to the upper portion of the outer supporting framework and to the upper portion of the pole. Thus, the lateral pressure exerted by the contained liquid on the outer walls could be resisted by an inwardly directed force along the upper portion of the walls. Other similar arrangements were necessary to provide walls that would withstand the outward pressure of the contained liquid.

The present invention contemplates a structure which is well adapted to contain a liquid, such as water, above a supporting surface. The structure is provided with a liquid containing member which is dimensioned to conform, at least in part, to a curve defined by the formula dx/ dy=y 1-3 where x and y represent respectively abscissa and ordinate values of points in the curve. By virtue of this configuration, the liquid containing member need only be supported by an upwardly directed force since all portions of the member when containing a liquid are subject to equal tension. A horizontally disposed supporting member is spaced above the supporting surface for connection to the liquid containing member, and to provide an upwardly directed supporting force for the wall portion thereof.

The configuration or shape which is characteristic of all or a part of the liquid containing member is determined by the formula dx/dy=y /1y I have determined that a tensile member disposed along a curve defined by this formula will be placed in equal tension at all points since the contained liquid will be held in static equilibrium. The radius of curvature of the tensile member is inversely proportional to the depth of the contained liquid and therefore inversely proportional to pressure since pressure varies in direct proportion to depth. Thus, the tension on all portions of the tensile member is equal. If the tensile member is constructed from a rigid material either the entire tensile member or portions thereof can be formed according to the specified formula. Such a liquid container, however, would still be supported only by an upwardly directed force.

Accordingly, it is an object of this invention to provide a novel liquid container which is particularly adapted to contain liquids above a supporting surface.

Another object of this invention is to provide a liquid container wherein the liquid containing member is supported only by upwardly directed forces.

Another object of this invention is to provide a liquid container which does not require a framework for its lateral support thereby obviating the necessity of complicated braces, stakes and the like.

And still another object of this invention is to provide a novel structure for containing liquids above a supporting surface, which structure may be adapted for relatively deep containers or relatively shallow containers.

And yet another object of this invention is to provide a liquid container having curved side Walls wherein the curvature of the walls is directly proportional to the depth of the contained liquid.

A further object of this invention is to provide a liquid container having a curved surface wherein the curvature at any point on the surface is directly proportional to the pressure exerted at that point by a contained liquid.

A further object of this invention is to provide a novel structure for containing liquids above a supporting surface wherein the structure is in static equilibrium when containing a liquid.

A still further object of this invention is to provide a liquid container which may be economically manufactured, is simple in construction, and which has a long service life.

In the drawings:

FIG. 1 is a sectional view of structure containing a liquid above a supporting surface and constructed in accordance with one embodiment of the present invention.

FIG. 2 is a schematic view of a longitudinally sectioned hypothetical tube which illustrates the laws of physics upon which the present invention is based.

FIG. 3 is a schematic view of another longitudinally sectioned hypothetical tube similar to the tube shown in FIG. 2 but differing therefrom in the size of the diameter of the tube.

FIG. 4 is a view of a geometrical figure used in the derivation of the formula necessary for the practice of this invention.

FIG. 5 is a view similar to FIG. 4, but one in which a mathematical operation has been performed upon the illustrated geometrical figure.

Referring now to the drawings in detail, and particularly FIG. 1, reference character designates a liquid container constructed in accordance with this invention and which is supported on a level solid base 12. A membrane or tensile member 14, having a bottom a and curved side walls 1512, contains a liquid 16, such as water, above the base. A means 18 is provided for supporting the member 14 with only an upwardly directed force. In the embodiment of the invention shown in the drawings, this means takes the form of a column base 20 which is positioned on the level base 12. A vertically upstanding column 22 is secured at its lower portion to the column base 20. A horizontally disposed beam 24 is secured in a suitable manner to the vertical column 22. The member 14 is secured to the beam 24 in a suitable manner either at or above the surface 26 of the liquid 16. The particular curvature of the member 14 is defined by the formula dx/dy=y /ly as will be explained in more detail hereinafter.

It will now be demonstrated why the curvature of the tensile member 14 must be directly proportional to the pressure of the contained liquid in a variable radius member if equal tension is maintained throughout the member. Referring now to FIG. 2, it will be seen that for static conditions a thin walled, cylindrical tube 28 having a radius r will be considered to be entirely filled with a liquid 30 having a pressure I. The tube 28 is considered to have a unit length and to be cut in half 1011- gitudinally. Point A is considered to be the lowermost point along the longitudinal face 32 of the tube 28 and to be positioned one unit length away from the cross sectional face 34 of the tube 28. Point B is considered to be a point falling within face 34 and oppositely disposed from point A. It is then desired to determine the tensile force T exerted on an area bounded by line AB and radius r. According to a well known law of physics, force is equal to area multiplied by pressure. Accordingly, the radius r multiplied by AB multiplied by P equals T. Since line AB is equal to unit length, the tensile force T is equal to r multiplied by P or rP.

A second similar tube 36 may be considered to have a radius r in which 1' is either larger or smaller than 1'. In tube 36 the tensile force T exerted on an area bounded by unit lentgh AB and radius r is the same as in the case of the first tube 28 and a pressure P is exerted therein. The tensile force T for the tube 36 will equal r P Accordingly, by substitution, IP is equal to r P and r/r is equal to P /P.

By definition, curvature K is equal to the reciprocal of the radius of curvature. Therefore, in the case of two tubes 28 and 36 l/K/l/K is equal to P /P and K /K is equal to P /P. Thus, it is clearly seen that the curvature K of a variable radius tensile member must be directly proportional to the pressure P exerted thereon if equal tension is to be maintained all along the member.

It will now be shown how the formula dx/dy=y /1-y is derived and how a curve according to this formula is generated. Referring now to FIG. 4, a right triangle 44 having an ordinal side 46 along the y-axis equal to y and a hypotenuse 48 equal to l/y is shown. Thus, the ordinal side 46 may be considered to represent the curvature of the tensile member 14 in FIG. 1 and the hypotenuse may then be considered the radius of curvature of such tensile member. Point C represents the center of curvature which may be said to move horizontally in the plane corresponding to the surface of the liquid 16 in the container 10, and to occupy at consecutive times during such movement, the points designated C C C and C; as shown in FIG. 1. It will be apparent that as the curve corresponding to the curvature of the tensile member 14 is generated, the curvature K (or in the triangle 44, y), being directly proportional to pressure (or to depth) of the liquid, will increase as the side of the tensile member progresses downwardly from the surface of the contained liquid to the bottom thereof. The radius of curvature, represented by the line CG of triangle 44 will, on the other hand, constantly decrease since, by definition, it is the reciprocal of the curvature.

In generating the curve which the illustrated side 15b of the tensile member 14 should describe, the point C (center of curvature) will move horizontally from a point C at which X is minus infinity, if it be assumed that the x-axis lies in the plane of the surface of the liquid and corresponds to the abscissa side of triangle 44, to a point C.,, at which X equals 0. The latter point lies in the vertical plane containing the bottom tangent point of the membrane 14 from which the horizontal dimensions of the membrane are measured. This movement of the center of curvature, C, and the manner in which the triangle 44 varies with such movement is represented by the dashed lines superimposed on FIG. 1. It will be apparent in referring to FIG. 1, that y, the curvature of the tensile membrance, may also serve as an expression of the vertical dimensions of the membrane. The hypotenuse 48 corresponding to the radius of curvature of the triangle 44 forms an angle, theta (0), with the abscissa side along the x-axis. An arc G having a radius l/y is generated by movement of the hypotenuse 48.

If all sides of the triangle 44 are multiplied by y, as seen in FIG. 5, the triangle 44 will have as the abscissa 45 a value of /1 y and as the ordinal side of the triangle 44 a value of y and for the hypotenuse a value of 1. The center of curvature is again represented by the letter C and any point on the arc G is represented by the letter G If it be assumed that the total depth of liquid in the tensile member is 1, then as point G moves from (0.5990701, 0) through (0, 1) to (-0.5990701, 0) the upper half of an oval is described. The center of curvature C moves along the x-axis from minus infinity, through a point where x is equal to zero, to plus infinity.

If it is then desired to mathmatically describe the motion of the point G as it moves from (0.5990701, 0) through (0, 1) to point (0.5990701, 0) as the center of curvature moves along the x-axis, the formula for the movement of the point G can best be described using ax and dy. By similar triangles as shown in FIG. 5, it will then be seen that the movement of point G is described by the formula dx/dy=y /ly It will be seen from an examination of FIG. 5 that y =sine 0 and by substituting this expression into the formula dx/dy=y /ly the formula x: /2f /sine 0:10 may be derived. In examining the above formula, it will be seen that all real values of y lie between +1 and -1. Simiq larly, it will be seen that all real values of x lie between 0.5990701 and 0.599070l.

When the depth of the liquid is assumed to be 1, the total area circumscribed by the complete oval described by -movement of point G as described above may be shown to be 2 and the area of the lower half of the oval, thus, to be 1. By numerical parabolic approximation, values for x were calculated from the basic derivative equation dx/dy=y /ly These values as a function of y are set forth in the following table. It will be noted that y is expressed as a percentage of the total depth of a contained liquid.

5990701 35 5847321 70 4780613 5 5990284 40 5776182 75 4471123 5987368 45 5684229 80 4094614 5979450 50 5568281 85 3628457 5964025 55 5424740 90 3029587 5938574 60 5249361 95 2189313 5900544 65 5036913 100 Zero Referring again to FIG. 1, it will be noted that if the tensile member 14 is dimensioned according to the formula dx/dy=y /ly the curvature y of the member 14 at any point thereon will be directly proportional to the depth of the liquid 16 at such point and will also be directly proportional to the pressure exerted by this liquid at such point. For use of this invention in an above ground swimming pool, it will be seen that the depth of the liquid 16 may be relatively great as compared to the width. For use of the invention in an above-the-ground liquid container such as a wading pool, the curvature of the side walls of the liquid container may still be dictated by the formula dx/dy=y /1-y but the portion of the member 14 which rests upon the base 12 will be proportionately greater if the same total length tension member is used. The tensile member 14 at the point at which it is attached to the horizontally disposed member 24, which may be the liquid surface 26, has a curvature of zero, being a straight line. Thus, the radius of curvature would be infinitely great. Also, at the surface of the liquid, the liquid pressure would be zero. As the tensile member 14 descends below the plane of the liquid surface 26 both the liquid pressure and curvature increase directly proportional to the depth of the liquid and the radius of curvature decreases. At one hundred percent of the liquid depth, which will be the bottom tangent point 50, the radius of curvature CG has decreased until it is equal to the liquid depth. The center of curvature as has hereinbefore been stated, does not remain stationary as the curve of the tensile member 14 is generated. If a complete U-shapecl tensile member (one-half of an oval) were to be generated, the center of curvature C would move along the line of the liquid surface 26 or, graphically, along the x-axis from negative infinity to positive infinity. It is also apparent that as the liquid depth increases, the curvature also increases in direct proportion thereto so that a curve of equilibrium is developed in which the curvature is directly proportional to the liquid pressure. Thus, the tensile member 14 is subjected to equal tension at all points from the surface of the liquid to the lowermost depth of the contained liquid.

If the tensile member 14 is a flexible material which has a tensile strength sufficient to withstand the tensile stresses placed upon it, it may be used to contain the liquid 16 with only an upwardly directed force. The material used for the membrane 14 is correctly dimensioned with respect to the depth of the liquid to be contained so that when an upwardly directed force is exerted by the horizontally disposed beam 24, the contained liquid 16 will cause the member 14 to form a curved surface having a curvature according to the basic formula dx/dy=y /1y The liquid pressure exerted by the contained liquid 16 will do this only if the di mensions of the tensile member 14 are correctly chosen. If the correct length of material 14 is used and the container 10 is filled with liquid 16, the resultant hydraulic forces will cause the member 14 to form the shape of the prescribed curve, because only this curvature will be in static equilibrium.

It is also within the scope of the present invention to form the tensile member 14 from a rigid material. If the member 14 is rigid, forming it to the prescribed curve will result in the exact required length of material being used which will give the desired condition, namely, that the side wall portion of the member 14 will be supported only by a vertical force exerted along its upper edge. If a rigid member is used, it is possible to provide the container 10 with a wall having either all or part thereof formed according to the prescribed formula. With respect to the sole purpose of resisting hydraulic pressures there is no preference as to the flexibility or rigidity of the tensile member 14, as long as the length or amount of material is used which will fit the prescribed curve. Also, it is apparent that the material chosen should be of a thickness and strength which will withstand over a requisite time the tension exerted upon it by hydraulic pressure from the contained liquid. If desired, the liquid container '10 may have a circular configuration, in a honizontal plane. However, if it is desired to construct the liquid container 10 so that it has a square or rectangular configuration, corners may be easily formed therefor by joining the tensile member of one side wall to the tensile member of an adjoining wall along the line of intersection of the two curved surfaces.

From the foregoing, it is apparent that the present invention provides a liquid container which is particularly adapted to contain liquids above a supporting surface. The liquid container is provided with sides having a curvature dictated by the formula dx/dy=y /1y The use of this formula to form the sides of the liquid container provides for the curvature of the side walls to be directly proportional to the depth of the contained liquid, and, a portion, directly proportional to the pressure of the liquid. Since the'curvature of the side walls varies according to the depth of the liquid, the tension of the wall, which is exerted thereon by hydraulic pressures, is equal throughout the entire wall surface. The use of this particular formula also allows the walls of the liquid con-tainer to be supported only by an upwardly directed force. This upwardly directed force for the walls of the container will obviate the necessity for the complicated braces and supports that were formerly required by above-the-gro-und liquid containers, such as swimming pools. Finally, it will be apparent that the present invention provides a liquid container well adapted for use as an above the ground swimming pool, that is economical to construct, simple in its elements, and which has a long trouble-free service life.

Changes may be made in the combination and arrangement of parts or elements as heretofore set forth in the specification and shown in the drawings, it being understood that changes may be made in the precise embodiment disclosed without departing from the spirit and scope of the invention as defined in the following claims.

I claim:

1. An open-topped container positioned above a supporting surface and adapted to be filled with liquid, comprising:

a generally planar base adapted to rest upon the supporting surface;

side walls extending upwardly from the base, each of said side walls being curved throughout the height thereof in accordance with the formula wherein x and y are abscissa and ordinate points, gaging the supporting surface and having the other respectively, on the respective side wall; and end in engagement with the upper ends of said side vertically disposed support means having one end enwalls to support said side walls by an upwardly dig aging the supporting surface and having the other meted f end in engagement with the upper end of each side 5 wall to support said side walls by an upwardly di- References Cited by the Examiner rected form Only UNITED STATES PATENTS 2. An open-topped, relatively rigid material container for containing a liquid above a supporting surface, corn- 9961453 6/1911 Callahanprising: 10 1,044,672 11/1912 Lohle 220- 1Z a generally planar base adapted to rest upon the sup- 0,199 1 /1914 Jagsc-hitz 220- 12 porting surface; 2,562,602 7/1951 Caquot 220-1 side walls extending upwardly from the base, each of FOREIGN PATENTS said side walls being curved from the base in accordance with the formula dx/dy:y /1y wherein x and y are abscissa and ordinate points, gelsdpectively, on the respective curved side wall; THERON E CONDON, Primary Examiner. vertically disposed support means having one end en- GEORGE E. LOWRANCE, Examiner.

15 906,895 3/1954 Germany. 1,031,067 5/1958 Germany. 

1. AN OPEN-TOPPED CONTAINER POSITIONED ABOVE A SUPPORTING SURFACE AND ADAPTED TO BE FILLED WITH LIQUID, COMPRISING: A GENERALLY PLANAR BASE ADAPTED TO REST UPON THE SUPPORTING SURFACE; SIDE WALLS EXTENDING UPWARDLY FROM THE BASE, EACH OF SAID SIDE WALLS BEING CURVED THROUGHTOUT THE HEIGHT THEREOF IN ACCORDANCE WITH THE FORMULA 